Synthesis Problem of Transverse Speed and Archimedes’ Principle

Summary: A Synthesis Problem combining Transverse velocity, Archimedes’ principle, and (though knowledge of it is optional) fundamental frequencies. As noted in the solution, the portion needing knowledge on fundamental frequencies may be solved by harmonics (and some inventivity.) Do try to solve it first before looking at the solution.

Problem abbreviated from Sears and Zemansky’s University Physics with Modern Physics 13th ed. Problem 15.81